When a moderator sends a message to a user, the message and all followup are available in the moderation tools. When a moderator contacts a CM through the site, on the other hand, the contact is recorded (good) but the response is via email to the moderator who made the request. This makes it harder for other moderators to track, and makes it hard for anybody to look up the results if they're needed later. Using an annotation to record the response doesn't feel quite right, but messages shared in moderator chat rooms can be hard to find later.
I'd like to see message history for CM contacts that is similar to the message history for user contacts. (It should be linked in the same place.) I'm guessing that the CM responses are being sent from a management tool external to the particular SE site, so I don't know how hard this integration would be. User responses via email end up in the history if I understand correctly, so I'm hoping there's something to hook into for CM responses via email.